Convexity and translational invariance constraint on the exchange-correlation functional

Abstract

Knowledge of the properties of the exchange-correlation functional in the form $\frac{1}{\lambda }{v}_{xc}([{\rho }_{\lambda }],\frac{\mathbf{r}}{\lambda })$, where ${\rho }_{\lambda }(\mathbf{r})=$ ${\lambda }^3\rho (\lambda \mathbf{r}),$ is important when expressing the exchange-correlation energy as a line integral (van Leeuwen and Baerends, Phys. Rev. A {\bf 51}, 170 (1995)). With this in mind, it is shown that in the low density limit This inequality is violated in the local-density approximation.

5 pages, REVTeX, to appear in Phys. Rev. A